Artificial intelligence (AI) has been successfully applied in industry for decades, ranging from the emergence of expert systems in the 1960s to the wide popularity of deep learning today. In particular, inexpensive computing and storage infrastructures have moved data-driven AI methods into the spotlight to aid the increasingly complex manufacturing processes. Despite the recent proverbial hype, however, there still exist non-negligible challenges when applying AI to smart manufacturing applications. As far as we know, there exists no work in the literature that summarizes and reviews the related works for these challenges. This paper provides an executive summary on AI techniques for non-experts with a focus on deep learning and then discusses the open issues around data quality, data secrecy, and AI safety that are significant for fully automated industrial AI systems. For each challenge, we present the state-of-the-art techniques that provide promising building blocks for holistic industrial AI solutions and the respective industrial use cases from several domains in order to better provide a concrete view of these techniques. All the examples we reviewed were published in the recent ten years. We hope this paper can provide the readers with a reference for further studying the related problems.